Sentence examples for exists a subnet of from inspiring English sources

Hence, there exists a subnet of such that.

Since is compact valued, there exists a subnet of such that.

There exists a subnet of such that w*-converges to μ for some invariant mean μ on B(S).

Since are lower -continuous, we note that for any neighbourhood of the origin in, there exists a subnet of such that (3.6).

The above argument shows that, for every subnet of, there exists a subnet of such that { T μ α β x } Δ-converges to T μ x(= Px).

Since are lower -continuous, it follows that for any neighbourhood of the origin in, there exists a subnet of such that (3.20).

Thus, there exists a subnet {x β } of {x α } such that x ∉ A (C, {x β }), and so lim sup β d x, x β ) > ρ > r(C, {x β }) for some ρ > 0. By (i), there exists a subnet { x γ β } of {x β } satisfying d ( x, x γ β ) ≥ ρ for all β.

By assumption, there exists a subnet { x η } of { x γ β } Δ-converging to x.

If lim sup α d x, x α ) > ρ for some ρ > 0, then there exists a subnet { x β α } of {x α } such that d ( x, x β α ) ≥ ρ for all α.

In view of (2.2), we arrive at μ t ∥ x t − x ∗ ∥ 2 ≤ 0. This implies that there exists a subnet { x t α } of { x t } such that x t α → x ∗.

Proof Since { x t } is bounded and E is reflexive, there exists a subnet { x t α } of { x t } such that x t α ⇀ p as t α → 0. Put g ( x ) = lim sup n → ∞ Φ ( ∥ x t α − x ∥ ), ∀ x ∈ E. (2.5).